Question

What is the observed value of the test​ statistic? (Find the test statistic for ModifyingAbove p with caret 1minusModifyingAbove p with caret 2​, where ModifyingAbove p with caret 1 is the proportion over the sample of people using the nicotine gum and ModifyingAbove p with caret 2 is the proportion over the sample of people using the​ placebo.)

Answer 1

The test statistic is
`z=\frac{\hat p_(1)-\hat p_(2)}{\sqrt{P(1-P)[(1)/(n_(1))+(1)/(n_(2))]}}`.

Explanation:

The test statistic for hypothesis test for the significant difference between two proportions is:

`z=\frac{\hat p_(1)-\hat p_(2)}{\sqrt{P(1-P)[(1)/(n_(1))+(1)/(n_(2))]}}`

The combined proportions P is computed using the formula:

`P=(n_(1)\hat p_(1)+n_(2)\hat p_(2))/(n_(1)+n_(2))`

Here,

Sample 1 represents the proportion over the sample of people using the nicotine gum.

Sample 2 represents the proportion over the sample of people using the​ placebo.